determine if these lines are parallel, perpendicular, or neither
2x+5y=8 and 5x+2y=2
To determine whether these lines are parallel, perpendicular, or neither, we can compare their slopes. The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope of the line.
Let's rewrite both equations in slope-intercept form:
For the first equation, 2x + 5y = 8:
1. Subtract 2x from both sides: 5y = -2x + 8
2. Divide both sides by 5: y = (-2/5)x + 8/5
The slope of the first equation is -2/5.
For the second equation, 5x + 2y = 2:
1. Subtract 5x from both sides: 2y = -5x + 2
2. Divide both sides by 2: y = (-5/2)x + 1
The slope of the second equation is -5/2.
Since the slopes of the two lines, -2/5 and -5/2, are not equal, the lines are not parallel.
To determine if the lines are perpendicular, we can check if the product of their slopes is equal to -1. If it is, then the lines are perpendicular.
Let's multiply the slopes of the two lines:
(-2/5) * (-5/2) = 1
Since the product of the slopes is not equal to -1, the lines are not perpendicular either.
Therefore, based on the calculation, the lines 2x + 5y = 8 and 5x + 2y = 2 are neither parallel nor perpendicular.